Values of modulus of elasticity (MOE, the ratio of stress, i. e., force per unit area, to strain, i. e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data (read from a graph in the article "Effects of Aggregates and Microfillers on the Flexural Properties of Concrete"â ). MOE 29.8 33.2 33.7 35.3 35.5 36.1 36.2 36.3 37.5 37.7 38.7 38.8 39.6 41.0
Strength 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0
MOE 42.8 42.8 43.5 45.6 46.0 46.9 48.0 49.3 51.7 62.6 69.8 79.5 80.0
Strength 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
(a) Construct a stem-and-leaf display of the MOE values. (Round each value down to the nearest whole number. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values. Split the stems, placing leaves 0 to 4 on the first stem and leaves 5 to 9 on the second stem of the same value. Use the tens digit as the stem and the ones digit as the leaf.)
stem leaf
2
2
3
3
4
4
5
5
6
6
7
7
8
8
Comment on any interesting features. (Select all that apply.)
There is some positive skew in the data.
There is a reasonably large amount of variation in the data.
There is a small amount of variation in the data.
There is some negative skew in the data.
There are some potential outliers.
(c) Use the accompanying Minitab output to obtain the equation of the least squares line for predicting strength from modulus of elasticity. (Enter your slope to five decimal places, and your intercept to four decimal places.)
Predictor Coef Stdev t-ratio P
Constant 3.2925 0.6008 5.48 0.000
mod elas 0.10748 0.01280 8.40 0.000
s = 0.8657 R-sq = 73.8% R-sq(adj) = 72.8%
Analysis of Variance
SOURCE DF SS MS F P
Regression 1 52.870 52.870 70.55 0.000
Error 25 18.736 0.749
Total 26 71.605
y =
Predict strength for a beam whose modulus of elasticity is 44. (Round your answer to two decimal places.)
(d) What are the values of SSE, SST, and the coefficient of determination? (Enter your answers to three decimal places.)
SSE=
SST=
r2=